3‐D local imaging utilizing paraxial ray‐traced green's functions

Abstract

3D prestack imaging represents, potentially, the highest quality imaging method in seismic. The main problem has been the large demand on computer resources that this method requires. A solution to this problem lies in an imaging method which concentrates the use of computer resources on the imaging of only local regions of interest in the subsurface. Such a method exists. It is imaging by use of the backpropagation Kirchhoff integral (Wapenaar, et.a1.,1989) and the generation of the backpropagation Green’ s function by ray tracing (KehoJ988) (ZhuJ988). The ray traced Green’ s functions are “event” oriented and directly relate subsurface features with seismic events in the prestack data. These events are then selectively backpropagated and focused by the Kirchhoff integral in the local region of the subsurface from which the ray traced Green’ s functions where generated. However, the ray tracing required in even limited local imaging can be quite large for realistic 3D seismic surveys. One needs ray trace information from all combinations of receiver and image points for every shot. We, therefore, use paraxial ray tracing and ray extrapolation and interpolation schemes in both the receiver domain and the image domain. These interpolation schemes drastically reduce the amount of ray tracing which is necessary. The processing time now becomes basically dependent on the computation of an imaging kernel instead of ray tracing. This can easily represent a savings in processing time of two orders of magnitude. It also now puts the problem of further reduction on the computation of an imaging kernel and not on ray tracing which depends on the model complexity and the ray trace algorithm efficiency. Of course, the method requires a numerical model as a basis for ray tracing. This model must be obtained by other standard processing methods such as stacking, poststack migration and velocity analysis. It will only be an approximation to the correct model; but one only needs a good estimate of the subsurface between the receiver arrays and the local image region. The ray paths indicate which parts of the model are involved. Finally, the limitations of the accuracy of ray tracing in seismic, as for example in diffraction and in caustic regions, are greatly outweighed by the advantage of being able to perform local imaging. Also additional information obtained by ray tracing can be utilized. For example, information about illumination of the image by the shot, illumination of the receivers by the scattered wave from the image and the wavefront information in both the image and receiver domain can be utilized. We use such information to generate “quality factors” for the image points, to determine angular dependency of the scattering coefficients and to perform data selection. A companion paper to be presented by Kinneging and Geerlings discusses the application of the back propagtion method in 3D prestack redatuming of seismic data.